In a right-angled triangle ABC, the angle between the bisector CK and the height CH, drawn from the vertex

In a right-angled triangle ABC, the angle between the bisector CK and the height CH, drawn from the vertex of the right angle C, is 15 °. AB = 12 cm.Find side BC if you know that point K lies between A and Н.

1. Angle ACK = 90 °: 2 = 45 °, since the bisector CК divides the right angle C into two equal parts.

2. Angle АСН = 45 ° + 15 ° = 60 °.

3. Angle AНС = 90 °, since CH is the height.

4. We calculate the value of the angle A, based on the fact that the total value of the inner angles of the triangle is 180 °:

Angle A = 180 ° – 60 ° – 90 ° = 30 °.

4. The BC leg is located opposite an angle of 30 °, therefore its length, according to the properties of a right-angled triangle, is half the hypotenuse AB.

BC = 12: 2 = 6 cm.

Answer: the length of the BC leg is 6 cm.